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We present a reduction theory for first order Lagrangian field theories which takes into account the conservation of momenta. The relation between the solutions of the original problem with a prescribed value of the momentum and the solutions of the reduced problem is established. An illustrative example is discussed in detail., Comment: v2: a few references added, some typos corrected

We discuss a new geometric construction of port-Hamiltonian systems. Using this framework, we revisit the notion of interconnection providing it with an intrinsic description. Special emphasis on theoretical and applied examples is given throughout the paper to show the applicability and the novel contributions of the proposed framework., Comment: This article supersedes the second part of arXiv:1702.08596. v2: a few references added

Dirac structures and Morse families are used to obtain a geometric formalism that unifies most of the scenarios in mechanics (constrained calculus, nonholonomic systems, optimal control theory, higher-order mechanics, etc.), as the examples in the paper show. This approach generalizes the previous results on Dirac structures associated with Lagrangian submanifolds. An integrability algorithm in the sense of Mendela, Marmo and Tulczyjew is described for the generalized Dirac dynamical systems under study to determine the set where the implicit differential equations have solutions., Comment: this article supersedes the first part of arXiv:1702.08596

We provide a generalization of the notion of Dirac system by using Morse families to intrinsically embrace the dynamics associated with different physical systems such as constrained variational calculus, optimal control, Lagrangian mechanics, etc., from both the Lagrangian and the Hamiltonian viewpoint. Besides, we introduce a geometric construction of Port-Dirac systems and use it to describe the interconnection of Dirac systems. Special emphasis on theoretical and applied examples is given throughout the paper to show the applicability of the proposed framework., Comment: This paper has been split into arXiv:1804.04951 and arXiv:1804.04949

In this paper, we will see that the symplectic creed by Weinstein "everything is a Lagrangian submanifold" also holds for Hamilton-Poincar\'e and Lagrange-Poincar\'e reduction. In fact, we show that solutions of the Hamilton-Poincar\'e equations and of the Lagrange-Poincar\'e equations are in one-to-one correspondence with distinguished curves in a Lagrangian submanifold of a symplectic manifold. For this purpose, we will combine the concept of a Tulczyjew triple with Marsden-Weinstein symplectic reduction., Comment: 26 pages

This paper contains results on geometric Routh reduction and it is a continuation of a previous paper where a new class of transformations is introduced between Lagrangian systems obtained after Routh reduction. In general, these reduced Lagrangian systems have magnetic force terms and are singular in the sense that the Lagrangian does not depend on some velocity components. The main purpose of this paper is to show that the Routh reduction process itself is entirely captured by the application of such a new transformation on the initial Lagrangian system with symmetry., Comment: To appear in Journal of Geometric Mechanics

In this paper, some new aspects related to Routh reduction of Lagrangian systems with symmetry are discussed. The main result of this paper is the introduction of a new concept of transformation that is applicable to systems obtained after Routh reduction of Lagrangian systems with symmetry, so-called magnetic Lagrangian systems. We use these transformations in order to show that, under suitable conditions, the reduction with respect to a (full) semi-direct product group is equivalent to the reduction with respect to an Abelian normal subgroup. The results in this paper are closely related to the more general theory of Routh reduction by stages., Comment: 23 pages

The nuclide 18F disintegrates to 18O by beta+ emission (96.86%) and electron capture (3.14%) with a half-life of 1.8288 h. It is widely used in nuclear medicine for positron emission tomography (PET). Because of its short half-life this nuclide requires the development of fast measuring methods to be standardized. The combination of LSC methods with digital techniques proves to be a good alternative to get low uncertainties for this, and other, short lived nuclides. A radioactive solution of 18F has been standardized by coincidence counting with a LSC, using the logical sum of double coincidences in a TDCR array and a NaI scintillation detector. The results show good consistency with other techniques like 4Pi gamma and LSC.